1 Introduction

Until this point we have been concerned primarily with methods for analyzing single variables obtained from twin pairs; that is, with estimation of the relevant sources of genetic and environmental variation in each variable separately. Most studies, however, are not designed to consider single variables, but are trying to understand what factors make sets of variables correlate, or co-vary, to a greater or lesser extent. Just as we can partition variation into its genetic and environmental components, so too we can try to determine how far the covariation between multiple measures is due to genetic and environmental factors. This partitioning of covariation is one of the first tasks of multivariate genetic analysis, and it is one for which the classical twin study, with its simple and regular structure, is especially well-suited. In Chapter 1 we described three of the main issues in the genetic analysis of multiple variables. These issues include

1. contribution of genes and environment to the correlation between variables
2. direction of causation between observed variables
3. genetic and environmental contributions to developmental change.

Each of these questions presumes either a different data collection strategy or a different model or both; for example, analysis of measurements of correlated traits taken at the same time (question 1) requires somewhat different methods than assessments of the same trait taken longitudinally (question 3). However, all of the multivariate issues share the requirement of multiple measurements from the same subjects. In this chapter we direct our attention to the first issue: genetic and environmental contributions to observed correlations among variables. We describe twin methods for the other two questions in Chapters  - . The treatment of multivariate models presented here is intended to be introductory. There are many specific topics within the broad domain of multivariate genetic analysis, some of which we address in subsequent chapters. Here we exclude treatment of observed and latent variable means and analysis of singleton twins.